This is an old question, but I just came across this article so there is now a "direct from the Director" reason:
One question that people ask me a lot about Titanic, and I’m assuming
they ask you this a lot, is at the end, why doesn’t Rose make room for
Jack on the door?
And the answer is very simple because it says on page 147 [of the
script] that Jack dies. Very simple. . . . Obviously it was an
artistic choice, the thing was just big enough to hold her, and not
big enough to hold him . . . I think it’s all kind of silly, really,
that we’re having this discussion 20 years later. But it does show
that the film was effective in making Jack so endearing to the
audience that it hurts them to see him die. Had he lived, the ending
of the film would have been meaningless. . . . The film is about death
and separation; he had to die. So whether it was that, or whether a
smoke stack fell on him, he was going down. It’s called art, things
happen for artistic reasons, not for physics reasons.
Well, you’re usually such a stickler for physics . . .
I am. I was in the water with the piece of wood putting people on it
for about two days getting it exactly buoyant enough so that it would
support one person with full free-board, meaning that she wasn’t
immersed at all in the 28 degree water so that she could survive the
three hours it took until the rescue ship got there. [Jack] didn’t
know that she was gonna get picked up by a lifeboat an hour later; he
was dead anyway. And we very, very finely tuned it to be exactly what
you see in the movie because I believed at the time, and still do,
that that’s what it would have taken for one person to survive.